MinT - Best Known (159−37, 159, s)-Nets in Base 3

Best Known (159−37, 159, s)-Nets in Base 3

(159−37, 159, 464)-Net over F₃ — Constructive and digital

Digital (122, 159, 464)-net over F₃, using

1 times m-reduction [i] based on digital (122, 160, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 40, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(159−37, 159, 932)-Net over F₃ — Digital

Digital (122, 159, 932)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−37, 159, 58214)-Net in Base 3 — Upper bound on s

There is no (122, 159, 58215)-net in base 3, because

1 times m-reduction [i] would yield (122, 158, 58215)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2427 596164 339229 504741 734811 474868 734955 911965 903768 128970 856189 161461 163821 > 3¹⁵⁸ [i]